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Existence of solutions to the Poisson equation in L p -weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of L p , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.

Existence of solutions to the Poisson equation in L₂-weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.

Extremal problems for conditioned brownian motion and the hyperbolic metric

Rodrigo Bañuelos, Tom Carroll (2000)

Annales de l'institut Fourier

This paper investigates isoperimetric-type inequalities for conditioned Brownian motion and their generalizations in terms of the hyperbolic metric. In particular, a generalization of an inequality of P. Griffin, T. McConnell and G. Verchota, concerning extremals for the lifetime of conditioned Brownian motion in simply connected domains, is proved. The corresponding lower bound inequality is formulated in various equivalent forms and a special case of these is proved.

Familles d'opérateurs potentiels

Francis Hirsch (1975)

Annales de l'institut Fourier

Ce travail se compose de trois parties. Dans la première partie nous donnons quelques résultats sur les noyaux-mesure de Hunt sur R + . Nous caractérisons à ce propos les transformées de Laplace des fonctions logarithmiquement convexes et dé-crois-san-tes sur R + . Dans la deuxième partie, nous démontrons que, si μ est un noyau-mesure de Hunt sur R + et si ( P t ) t 0 est un semi-groupe à contraction dans un espace de Banach X tel que son générateur infinitésimal soit d’image dense, alors l’opérateur P t d μ ( t ) défini au...

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